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Arithmetic Geometry over Global Function Fields

Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer (Autoren)

Francesc Bars, Ignazio Longhi, Fabien Trihan (Herausgeber)

Buch | Softcover

XIV, 337 Seiten

2014 | 2014
Springer Basel (Verlag)
978-3-0348-0852-1 (ISBN)

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This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.

Cohomological Theory of Crystals over Function Fields and Applications.- On Geometric Iwasawa Theory and Special Values of Zeta Functions.- The Ongoing Binomial Revolution.- Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields.- Curves and Jacobians over Function Fields.

Erscheint lt. Verlag	4.12.2014
Reihe/Serie	Advanced Courses in Mathematics - CRM Barcelona
Zusatzinfo	XIV, 337 p.
Verlagsort	Basel
Sprache	englisch
Maße	168 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Cohomology theory • Drinfeld Modules • Gamma functions • L-functions • t-motives • Zeta and Multizeta functions
ISBN-10	3-0348-0852-6 / 3034808526
ISBN-13	978-3-0348-0852-1 / 9783034808521
Zustand	Neuware